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- CONTENTS 1988 - VOLUME 306 - SECTION I - N° 2
- .......... Page(s) .......... 59
- We prove that the Hecke eigenvalues of certain automorphic forms on the symplectic group are algebraic.
- .......... Page(s) .......... 67
- .......... Page(s) .......... 67
- We present here a common frame to a large class of commutative Banach algebras of bounded Radon measures, including abelian locally compact groups, Gel'fand pairs, generalized translations of Delsarte-Levitan associated with some Sturm-Liouville operators, homogeneous trees, as well as numerous natural situations associated with sequences of orthogonal polynomials. In this frame, and under the hypothesis of power-type growth, we prove among other results, an extension of a theorem of G. Choquet and J. Deny giving the constancy of bounded functions invariant with respect to a probability as well as well as related L1-type ergodic theorems.
- .......... Page(s) .......... 71
- In this Note we establish a spherical symmetry result for positive solutions of semi-linear elliptic equations of the type
in a sector-like domain with mixed boundary conditions. is a sector cut out of a ball by two planes; the angle measures the opening of this sector, and , where and are respectively the spherical and plane portions of the boundary . We assume that on while on . Spherical symmetry of any such u is proved when . On the other hand, for any we construct counter examples. Axial symmetry properties in more general geometries are also derived here. These results extend the Theorem of Gidas, Ni and Nirenberg for spheres to sector-like domains and mixed boundary conditions.
- .......... Page(s) .......... 75
- .......... Page(s) .......... 75
- We describe a generalization of the fixed point theorem for classical T-equivariant cohomology, where T is the circle group, valid in many infinite dimensional cases. The most important ingredient is the construction of a new form of equivariant cohomology for smooth T-manifolds which agrees with classical periodic equivariant cohomology for finite dimensional manifolds. This new cohomology theory has the property that restriction to the fixed point set induces an isomorphism for a large class of manifolds, including infinite dimensional manifolds like loop spaces of finite dimensional manifolds. For the classical theory this fixed point theorem is only true in finite dimensions. Our motivation comes from the ideas of Witten [9], Atiyah [1] and Bismut ([3], [4]) relating loop spaces and the index theorem and we mention, very briefly, some applications of the new theory to questions concerning loop spaces.
- .......... Page(s) .......... 79
- .......... Page(s) .......... 79
- We use the isoperimetric inequality for Gauss measure to show that a fonction on Rn whose gradient is integrable with respect to Gauss measure belongs to the Orlicz space L1 (Log L)1/2 of this measure. This complements the logarithmic Sobolev inequality of Gross.
- .......... Page(s) .......... 83
- .......... Page(s) .......... 83
- We investigate the non-parametric estimation of a multivariate regression function and its derivatives by kernel method. Rates of convergence are given under a strong uniform mixing condition. Particularly in the independent case, optimal rates (Stone [15]) are reached.
- .......... Page(s) .......... 87
- .......... Page(s) .......... 87
- All rational surfaces on a square are described by a control net made up of weighted points and vectors. The behavior of the control net by projective and affine transformations is established. Some examples are given as well as stable algorithms for computing any point for their use in CAD and CAM.
- .......... Page(s) .......... 93
- .......... Page(s) .......... 93
- We will use a computation model where executing a program on an input corresponds to calculating a product in a finite monoid. We will show that in this model the subsets of that can be recognized by nilpotent groups have exponential cardinality.
- COMPTES RENDUS DE L'ACADEMIE DES SCIENCES
- .......... Page(s) .......... I
- Théorie des nombres
- Algèbre
- .......... Page(s) .......... 63
- Théorie des groupes
- .......... Page(s) .......... 67
- Equations aux dérivées partielles
- Topologie
- .......... Page(s) .......... 75
- Probabilités
- .......... Page(s) .......... 79
- Statistique
- Analyse numérique
- Informatique théorique
- .......... Page(s) .......... 93
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